How to maintain driver positive values
Yes, though you may need to change the driver to a scripted expression (easy to do). See The Blender Documentation for more info.
I’m guessing you copy-pasted the driver.

Right-click the driven property (purple) and click edit driver.
In the appearing dialogue, change the mode from averaged sum to scripted expression.
Put an abs(...) around the variable now in the scripted expression field to take its absolute value. For example, if the variable was position the code should be abs(position).